Thermodynamics and Chemistry

CHAPTER 8 PHASE TRANSITIONS AND EQUILIBRIA OF PURE SUBSTANCES

8.2 PHASEDIAGRAMS OFPURESUBSTANCES 210

bc

350

360

370

380

390

400

0 50 100 150 200

.V=n/=cm^3 mol^1

T

Æ=

C

d c b a

Figure 8.11 Isobars for the fluid phases of H 2 O.a The open circle indicates the

critical point, the dashed curve is the critical isobar at220:64bar, and the dotted curve

encloses the two-phase area of the temperature–volume phase diagram.

Solid curves: a,pD 200 bar; b,pD 210 bar; c,pD 230 bar; d,pD 240 bar.

aBased on data in Ref. [ 124 ].

the left of this curve, the one-phase gas area lies to the right, and the critical point lies at the
top.
The diagram contains the information needed to evaluate the molar volume at any tem-
perature and pressure in the one-phase region and the derivatives of the molar volume with
respect to temperature and pressure. At a system point in the one-phase region, the slope
of the isotherm passing through the point is the partial derivative.@p=@Vm/T. Since the
isothermal compressibility is given byTD.1=Vm/.@Vm=@p/T, we have

TD

1

Vmslope of isotherm

(8.2.9)

We see from Fig.8.10that the slopes of the isotherms are large and negative in the liquid
region, smaller and negative in the gas and supercritical fluid regions, and approach zero at
the critical point. Accordingly, the isothermal compressibility of the gas and the supercrit-
ical fluid is much greater than that of the liquid, approaching infinity at the critical point.
The critical opalescence seen in Fig.8.7is caused by local density fluctuations, which are
large whenTis large.
Figure8.11shows isobars for H 2 O instead of isotherms. At a system point in the
one-phase region, the slope of the isobar passing through the point is the partial derivative
.@T=@Vm/p. The cubic expansion coefficient is equal to.1=Vm/.@Vm=@T /p, so we have

D

1

Vmslope of isobar

(8.2.10)